A 40-W instrument has a resistance of \(90\ \Omega\). On what voltage should it be operated normally?

Answer Details

To calculate the voltage required to operate the 40-W instrument with a resistance of 90 Ω, we can use Ohm's law, which states that the voltage (V) equals the product of the current (I) and the resistance (R): V = I × R. First, we need to calculate the current that flows through the instrument. We can use the formula for power (P) in terms of current and resistance: P = I^2 × R. Rearranging this equation, we get: I = sqrt(P / R). Substituting the values given in the problem, we get: I = sqrt(40 W / 90 Ω) ≈ 0.632 A Now we can use Ohm's law to find the voltage: V = I × R = 0.632 A × 90 Ω ≈ 56.9 V Therefore, the voltage required to operate the instrument normally is approximately 56.9 volts. (60V) is the closest to this value. Note that this is a simple example of how to apply Ohm's law to a practical problem. In real-life situations, the calculation may be more complicated, and other factors such as the temperature coefficient of resistance may need to be considered.